Beyond odious and evil
Number Theory
2014-05-27 v1
Abstract
In a recent post on the Seqfan list the third author proposed a conjecture concerning the summatory function of odious numbers (i.e., of numbers whose sum of binary digits is odd), and its analog for evil numbers (i.e., of numbers whose sum of binary digits is even). We prove these conjectures here. We will also study the sequences of "generalized" odious and evil numbers, and their iterations, giving in particular a characterization of the sequences of usual odious and evil numbers in terms of functional equations satisfied by their compositions.
Keywords
Cite
@article{arxiv.1405.6214,
title = {Beyond odious and evil},
author = {Jean-Paul Allouche and Benoit Cloitre and Vladimir Shevelev},
journal= {arXiv preprint arXiv:1405.6214},
year = {2014}
}